Link prediction finds the future or the missing links in a social–biological complex network such as a friendship network, citation network, or protein network. Current methods to link prediction follow the network properties, such as the node’s centrality, the number of edges, or the weights of the edges, among many others. As the properties of the networks vary, the link prediction methods also vary. These methods are inaccurate since they exploit limited information. This work presents a link prediction method based on the stochastic block model. The novelty of our approach is the three-step process to find the most-influential nodes using the m-PageRank metric, forming blocks using the global clustering coefficient and, finally, predicting the most-optimized links using maximum likelihood estimation. Through the experimental analysis of social, ecological, and biological datasets, we proved that the proposed model outperforms the existing state-of-the-art approaches to link prediction.

Complex Networks can depict a clear image of real-world systems. A real-world scenario can be represented a graph with interconnected layers - called a multi-layer network. Finding motifs can give an idea of the topology of complex systems and helps to understand the dynamics in the graphs. Looking at motifs as atoms of the network is helpful to analyze the relationship between nodes, and between layers. In this work, we suggest a sub-graph enumeration approach to find and count the motifs in multi-layer network. The proposed work has many application in graph mining, particularly to structure and dynamics of complex networks.

Complex networks model real-world relationships between entities where any two entities share more than one kind of relationship. Directed multilayer networks are used to represent such networks effectively, capturing the heterogeneity exhibited by the nodes and the directionality of relationships. The link prediction problem refers to predicting relationships (links) between the entities (nodes) that may arise in the future or identifying missing links to reconstruct the network. Our previous work proposed a novel block formation algorithm to determine future links between the blocks. This work proposes an intrablock link prediction technique within the blocks’ nodes exhibiting strong internal connectivity. The novelty of the proposed approach lies in extracting triads from a block using G–Trie by formulating a probabilistic model to predict the links between triads based on isomorphic properties, activity of nodes, and presence of common and influencer nodes. The experimental results on social, biological, and ecological datasets demonstrate that our hybrid framework achieved higher link prediction accuracy for both directed dense networks and sparse networks with lesser computational complexity.

Complex networks represent non-trivial topologies of connected natural and artificial systems. Revealing how information spreads within such multilayered systems is critical to the investigation of processes such as social influence, rumor spread, and epidemic spread. This article presents a clustering method based on a centrality-based measure of a multilayer personalized PageRank (m-PageRank) that aggregates node influence across layers to identify structurally and functionally cohesive clusters. The suggested framework supports realistic modeling of intra- and inter-cluster information propagation in complex networks. In addition, we examine the effects of clustering properties on diffusion efficiency and the epidemic threshold. Experimental verification shows that the m-PageRank-based clustering improves diffusion insight by effectively detecting influential nodes and tight communities, thus uncovering how enhanced clustering conditions the collective spread dynamics in multilayer networks.